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JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region (in sq. units), in the first quadrant bounded by the parabola \(y = 9x^2\) and the lines \(x = 0,y = 1\) and \(y = 4,\) is
- A \(7/9\)
- B \(14/3\)
- C \(7/3\)
- D \(14/9\)
Answer & Solution
Correct Answer
(D) \(14/9\)
Step-by-step Solution
Detailed explanation
Required area \( = \int\limits_{y = 1}^4 {\sqrt {\frac{y}{9}} dy} \) \( = \frac{1}{3}\int\limits_{y = 1}^4 {{y^{1/2}}dy = \frac{1}{3} \times \frac{2}{3}} \left( {{y^{3/2}}} \right)_1^4\)…
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